User GPS receiver architectures vary widely and can supply a wide variety of measurements in addition to pseudorange and continuous carrier phase, the two primary characteristic measurements from GPS. Pseudorange, xcfx81uk from Equation (1) below, is the receiver measurement of the geometric range to the satellite with degradation from satellite and receiver clock errors, the atmosphere and receiver errors. The second primary measurement of the receiver is the continuous carrier phase, xcfx86uk in Equation (2) below. Continuous carrier phase shares the same degradation factors as the pseudorange, but an additional uncertainty is added since the wavelength of the carrier is only 19 centimeters and has an integer ambiguity that is difficult to resolve in real-time.
As implied by Equations (1) and (2), a number of factors conspire to corrupt the pseudorange and carrier phase measurements for GPS. These errors are summarized below.
xcfx81uk=rukxc2x71uk+buxe2x88x92Bk+Iuk+Tuk+xcexdukxe2x80x83xe2x80x83(1)
xcfx86uk=rukxc2x71uk+buxe2x88x92Bk+Iuk+Tuk+NukxcexL1+"xgr"ukxe2x80x83xe2x80x83(2)
where
xcfx81uk≐the pseudorange from the user receiver, u, to the kth satellite
xcfx86uk≐the continuous carrier phase from the user receiver, u, to the kth satellite
1uk≐the line-of-sight from the user receiver, u, to the kth satellite
rukxc2x71uk≐the calculated range from the user receiver, u, to the kth satellite
bu≐the user receiver clock offset from GPS time
Bk≐the kth satellite clock offset from GPS time
Iuk≐the ionospheric delay along the line-of-sight from the user receiver, u, to the kth satellite
Tuk≐the tropospheric delay along the line-of-sight from the user receiver, u, to the kth satellite
Nuk≐the continuous phase cycle ambiguity from the user receiver, u, to the kth satellite
xcexL1≐the L1 carrier phase wavelength, 0.1903 meters
xcexduk≐the pseudorange measurement error
"xgr"uk≐the carrier phase measurement error
Clock errors are mostly due to the degradation associated with Selective Availability (SA). This intentional degradation corrupts the range accuracy by values up to several tens of meters. Studies shown it reasonable to assume that the overwhelming majority of SA errors are from clock perturbations. The US Government deactivated SA on May 2, 2000, indicating that it will not be enabled again.
Ionospheric delay is caused when the GPS signal encounters the ionosphere. The carrier wave is advanced while the code phase is delayed. These effects are partially corrected for the single-frequency user by the Klobuchar ionospheric parameters broadcast in the GPS message itself. Dual frequency receivers can, for the most part, remove these effects directly.
Tropospheric delay can be up to 30 meters for low elevation satellites due to GPS signal propagation through the lower atmosphere (troposphere). There are two primary components of the tropospheric delay, dry and wet. The dry component makes up about 90% of the total delay and can be modeled well with surface pressure data. The wet component is much more difficult to model and not well correlated with surface conditions. The wet term can add as much as 2-3 meters of uncorrected error on the GPS measurements.
Ephemeris errors occur when the reported satellite position does not match the actual position. The component of these errors along the line of sight to the user is usually less than a few meters.
Multipath errors are due to local reflections of the signal near the receiver and are tracked with delay, corrupting the range and phase measurements. These effects are very sensitive to the local environment. Tall buildings are the most commonly encountered source of the reflections that cause multipath interference.
Receiver noise is comprised of thermal noise, signal and modeling quantization. These errors are usually limited to about 1 meter for pseudorange and 1 mm for carrier phase.
Since many of the above-discussed errors are common-mode for receivers that are sufficiently proximal to one another, it is possible to use measurements from one GPS receiver at a known reference location to correct the measurements of the nearby xe2x80x9cmobilexe2x80x9d receiver (a mobile receiver may be in motion or stationary; xe2x80x9cmobilexe2x80x9d is meant to indicate its usual location being unfixed with respect to the earth""s surface). At the limit, for two receivers that share the same antenna, the only residual errors that would remain are due to receiver noise.
Using GPS measurements from one or more GPS receivers to correct another GPS receiver is called differential GPS (DGPS). Every DGPS system contains three system elements: 1) a single receiver or multiple GPS receivers at known reference (fixed) locations; 2) a mobile (unfixed) receiver; and 3) a communication link between the reference receiver(s) and the mobile unit.
Local-Area Differential GPS consists of a single reference station (a GPS receiver) at a known location measuring the errors in the pseudorange and broadcasting pseudorange corrections to mobile receiver users or a data processing and storage system via a data link. Other measurements and information from the satellites may also be received by the local-area differential GPS reference station and transmitted via the data link. Such other measurements/information includes the satellite almanac, ephemeris, carrier phase, pseudodoppler (commonly referred to as Doppler measurements or range rate), phase bias, frequency bias, clock offset, signal strength, local angles of elevation and azimuth, and others. The operating presumption is that errors observed by a mobile user are nearly identical to those observed by a nearby reference receiver. Errors typically excepted from this presumption are local phenomena such as multipath and receiver noise. In the extreme case where the location of the mobile unit and the reference station are the same, all error sources except for multipath and receiver noise cancel out.
Local-area differential GPS can reduce position errors to as little as 0.5 meters (with smoothing). However, local-area differential GPS systems suffer from a high sensitivity to the proximity of the user to the reference station. Beyond a separation of, typically, 100 kilometers the solution degrades to an unacceptable degree. As such, for functionally acceptable DGPS corrections to be available over the entire Coterminous United States (CONUS), over 500 stations are required.
The use of wide-area differential GPS for the aviation community is currently under development by the FAA and is called the Wide Area Augmentation System (WAAS). The data link employed by this system is a geostationary satellite, which has a semi-major axis of 42,000 km and a nearly zero degree inclination. The major advantage of this satellite orbit configuration is that it is synchronous with the rotation of the Earth and, therefore, is at all times in a practically fixed position relative to mobile receiver users and reference stations.
The principle behind wide-area differential GPS is the use of multiple GPS reference stations to form xe2x80x9cvectorxe2x80x9d corrections for each satellite in view of all or a subset of the GPS reference stations. The vector corrections are broken down into the components of the error sources to GPS. In a wide-area differential GPS system, the corrections include satellite ephemeris, satellite clock and the ionosphere. As in local-area differential GPS systems, multipath errors and receiver noise are not corrected, as these are purely local phenomena related exclusively to the mobile unit. The vector corrections are formed by making simultaneous measurements at multiple reference stations of the same GPS satellite observables. Observables that are recorded at the reference stations include pseudorange, pseudodoppler, carrier phase, and signal levels. Once the corrections are formulated, they are transmitted to geostationary satellites that re-broadcast the corrections to mobile users tracking the geostationary satellite. The mobile user tracks both the GPS satellites and the geostationary satellites and can thus derive pseudorange measurements not only from the GPS satellites but also the geostationary satellite. While the resultant GPS measurements, assisted by the broadcast corrections from the geostationary satellites, are more accurate, additional range sources may be used to supplement GPS. However, the vector corrections from the system are only available through the geostationary satellite. The wide-area system under development by the FAA is a xe2x80x9cclosedxe2x80x9d system meaning that the measurements are not directly available to mobile receiver users.
It is well known in the art that stand-alone GPS receivers are prone to a number of errors, some natural and some man-made, as discussed above. These errors generally delay the arrival of the signals in space, resulting in errors in the measured position of the receiver. These position errors make all subsequent dependent measurements, such as elapsed distance or instantaneous velocity, inaccurate. The United States Department of Defense (DoD) has routinely used Selective Availability (SA) to degrade position accuracy for civilian users of GPS. Although, as discussed above, SA was disabled in early May 2000, the inherent natural errors in the system still require corrective measures. Measurements of position, elapsed distance, or velocity based on stored waypoints are inherently inaccurate. In particular the accuracy (in terms of percentage, not magnitude) of these measurements is worse at lower speeds. Cyclists (xcx9c10 to 20 m/s), for example, suffer smaller errors than pedestrians (xcx9c1 or 2 m/s). Poor satellite visibility due to dynamic motion (e.g., while running) can further decrease accuracy and increase the need for corrective measures.
The previously employed technique for elapsed distance measurement was to take the absolute distance between two measured GPS waypoints. The elapsed distance measurement produced by this technique is consistently and inaccurately high, and can be significantly wrong if there is a satellite set switch (constellation change) as depicted in FIG. 1. The technique is especially error prone in the case of slow speeds, as shown in FIG. 2 and discussed below in further detail, and/or the presence of SA.
A system that provides accurate measurement of elapsed distance and instantaneous velocity is valuable to both commercial and recreational users. Differential GPS (DGPS), including both the Local-Area and Wide-Area systems discussed above, utilizes pseudorange corrections to improve accuracy. However, DGPS receivers are typically larger and more expensive. Accordingly, what is needed in the art are calibration techniques that allow for precise elapsed distance and instantaneous velocity measurements in real time without the required use of differential corrections.
In accordance with principles of the present invention, a method is disclosed of determining the distance traveled during an event by a mobile GPS receiver. The event comprises a plurality of epochs.
In a preferred embodiment, the method comprises receiving pseudorange data comprised of one of pseudorange differences or range rates. Each pseudorange difference, in turn, comprises a difference between a first pseudorange and a second pseudorange. The first pseudorange comprises the pseudorange between the receiver and a GPS satellite at a first epoch of the plurality of epochs. The second pseudorange comprises the pseudorange between the receiver and the GPS satellite at a second epoch of the plurality of epochs. The range rates comprise a range rate measurement taken by the receiver of the GPS satellite from the first epoch to the second epoch. Line-of-sight data comprised of at least one normalized vector between the receiver and the GPS satellite is then determined. Based on the pseudorange and line-of-sight data, incremental distance data is then determined. This determination comprises determining a linear algebraic solution of the pseudorange and line-of-sight data. The linear algebraic solution determination yields one of receiver position difference data or three-dimensional velocity data. This determination further comprises determining a root mean square of the receiver position difference data or three-dimensional velocity data. A sum over the event of the incremental distance data is then determined.
These functions are typically initiated and/or performed by software code modules stored in a memory associated with and executing on a processor.